If you like old school cyberpunk-ish stuff, you may really dig
Kurau: Phantom Memory. It's an anime from 2004 that's basically about a woman who, when she was 12, got caught up in a lab accident that caused her to end up possessed by alien entities from another dimension. She initially uses the resulting powers to take on merc work, but after one of the entities accidentally breaks free and creates itself a body, she finds herself on the run from people trying to capture the both of them for experimentation. Also, the moon is completely colonized, because why not. It's by Bones and has the same director as Full Metal Alchemist: Brotherhood and Alien 9, and it even has an 'okay' dub.
If you don't mind an anime that doesn't care about how absurd it is,
Speed Grapher may also be your bag. It's kind of all over the place but I found it entertaining the whole way through because it absolutely has no chill. The main character gains the power to blow things up with his camera and he constantly is on the run from various assassins whose fetish quite literally determine their super powers. Do I really need to say more?
Also, the opening is a fucking Duran Duran song.
Lastly, I feel required to mention
Lain, though you probably already know about it considering how (in)famous it is in how pretentious its fans are lol
I've also heard good things about stuff like Ergo Proxy, Texhnolyze, etc; but I haven't actually watched those myself yet so I don't wanna recommend something blind.